System Dynamics Modeling with STELLA software

Learning objectiveAfter this class the students should be able to:Understand basic concepts of system dynamics,Stock Variable;Flow Variable;Information Flow; Material Flow; andTime Delay;Understand how these basics elements interact with policies and decisions to determine the behavior of dynamic systems.

Time ManagementThe expected time to deliver this module is 50 minutes. 20 minutes are reserved for team practices and exercises and 30 minutes for lecture.

System DynamicsMethodology to study systems behavior

It is used to show how the interaction between structures of the systems and their policies determine the system behavior

Approach developed to study system behaviors taking into account complex structures of feedbacks and time delays

Warm-upEach team is invited to describe through any kind of diagram the process to fill a cup of water.

Imagine this as an exercise of operation management

(5 minutes)

Feedback refers to the situation of X affecting Y and Y in turn affecting X perhaps through a chain of causes and effects. Feedback Loop

\Its the time between the action and the result (consequence) of this action.

Time Delay

Causal Diagram

Population Dynamic

Basic ElementsThis methodology use five basics elements: Stock Variable;Flow Variable;Information Flow; Material Flow; andTime Delay

Object Oriented Language

A Model

Exploring a simple exampleTo explore modeling with STELLA, we will develop interactively with you, a basic model of the dynamics of a fish population. Assume you are the owner of a pond that is stocked with 200 fish that all reproduce at a fixed rate of 5% per year. For simplicity, assume also that none of the fish die. How many fish will you own after 20 years?

Stock - Fish InventoryWe begin with the first tool, a stock (rectangle). In our example model, the stock will represent the number of fish in our pond.This stock is known as a reservoir. In our model, this stock represents the number of fish we have in this time are in our the pondFigure 1Click here to open the stella software

What control the number of fishAs we assumed that the fish in our pond never die, we have one control variable: REPRODUCTION. We use the flow tool (the rightpointing arrow, second from the left) to represent the control variable, so named because it controls the states (variables).

Figure 2200 Fishes

ConverterNext we need to know how the fish in our population reproduce, that is, how to accurately estimate the number of new fish per annum. Remember? We assumed our fish population reproduce at 5% per year.

This can be represented as a transforming variable. A transforming variable is expressed as a converter, the circle that is second from the right in the STELLA toolbox.

Connector At the right of the STELLA, toolbox is the connector (information arrow). We use the connector to pass on information about the REPRODUCTION RATE to REPRODUCTION and another to pass on information from FISH population to REPRODUCTION.Figure 3

Our first modelOnce you draw the information arrow from the transforming variable REPRODUCTION RATE to the control and from the stock FISH to the control, open the control (REPRODUCTION) and converter (REPRODUCTION RATE) and type respectively 5/100 and the equation: REPRODUCTION RATE* FISHFigure 4200 5/100REPRODUCTION RATE*FISH

Run the modelWe get Figure 5. We see a graph of exponential growth of the fish population in your pond. Figure 5

What-if?From now on, the professor can practice what-if with the teams For example: What would happen if we decided to extract fish at a constant rate of 3% per year, and the reproduction rate varied with the fish population as it is seen in figure 6?

Figure 6

New model

ResultsFigure 7

Reference The Fifth Discipline. Peter Senge, Currency Doubleday, 1994, Chapter 5.

Modeling Dynamic Economic System. Ruth, M. & Hannon, B. Springer, 1997, Chapter 1

*Follow these instructions before you proceed. Then double click on the STELLA icon to open it. On opening STELLA, you will be faced with the HighLevel Mapping which we will not need now. To get to the Diagram Layer, click on the downwardpointing arrow in the upper lefthand corner of the frame. Now, on the task bar, click on the rectangle with your mouse, drag it to the center of the screen, and click again. Type in FISH. This is what you get in figure 1 in this slide.

*Click on the flow symbol, then click on a point about 2 inches to the left of the rectangle (stock) and drag the arrow to FISH, until the stock becomes dashed, and release. Label the circle REPRODUCTION. Figure 2 illustrates what we will have.

*The same clicking and dragging technique that got the stock on the screen will bring up the circle. Open the converter and enter the number of 0.05 (5/100).*Remember: open the objects by doubling clicking on it.*To display the results of our model, click on the graph icon and drag it to the diagram. If we wanted to, we could display these results in a table by choosing the table icon instead. Choose the variables that you are interest in analyze their behavior. Run the model. You can run the model by selecting RUN from the pulldown menu.